## Four “4”s

Here is something for U to think over…

# Can U get 64 using only two 4’s??

For Example :-

64using Four 4’s

(4 + 4) x (4 + 4) =64

64using Three 4’s

(4 x 4 x 4) =64

64using Two 4’s

( ? ? ) =64

Can U get the number 64 using** ONLY TWO **4’s??…

NOTE: * ONLY* Mathematical operations permitted are

Addition, Subtraction, Multiplication, Division, Exponentiation.

__________________________

**Solution(s) :** Checkout the **COMMENTS**.

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4^4=64. obv from four 4’s =)

ZogG said this on Wed, 10 Mar, 2010 at 12:40 PM |

@ZogG 4^4 = 4*4*4*4 = 256 (NOT 64)

Good Try!!

HINT:

Exponentiation includes squareroot too.

Right??.. C’mon lets see if U can get 64 now… 😉

cvs268 said this on Wed, 10 Mar, 2010 at 1:38 PM |

4^(4-4/4)

madhav k said this on Thu, 11 Mar, 2010 at 9:18 PM |

Good One!! 😉

Now try it with 2 Fours…

cvs268 said this on Thu, 11 Mar, 2010 at 9:28 PM |

4e2*4=64…… (4)^2*4=64

Mahesh said this on Fri, 12 Mar, 2010 at 2:07 AM |

U mean

Square(4)* 4?…64it is!!Good One!! 🙂

cvs268 said this on Fri, 12 Mar, 2010 at 9:08 AM |

Come on dude.. where does the 2 come in between in exponent? U need to use two 4’s ONLY!! And Square() is not a usual mathematical function.. If so, I have another most complicated one.. take this..

4^ceil(Inverse(0.4)) 😉

Manjunath said this on Fri, 12 Mar, 2010 at 10:02 AM

Got the answer!!! Its..

4 << 4 😉

Manjunath said this on Fri, 12 Mar, 2010 at 1:27 PM |

Woooo Hooooooo!!!!

Most Innovative answer man!!

Proud to be an Electronics Engineer!! 😉

Awesome!! But still one other solution remaining undiscovered…

cvs268 said this on Fri, 12 Mar, 2010 at 4:51 PM |

For the uninitiated can you please explain this function/operation that is used in this solution

4 < < 4 ?

Thanks!

Shankaree said this on Thu, 26 Dec, 2013 at 1:47 PM

The “<<" is a left shift. In binary i.e. base2 notation, a left-shift by one position is equivalent to multiplying by 2. Hence

4 << 4is 4 left shifted four times, i.e. doubled four times, which is 64.CVS268 said this on Thu, 26 Dec, 2013 at 2:41 PM

Take: 4^4!

4^4! = 4^24

Take sqrt(4^24):

=sqrt(4*4*4*……*4) [sqrt of 24 times 4].

=2*2*2*……*2 [24 times 2]

Again take sqrt(2*2*…*2)

=sqrt( (2*2) * (2*2) * (2*2) * ……) [sqrt of 12 pairs of 2]

=2*2*2*….*2 [12 times 2]

Again take sqrt(2*2*…*2)

=sqrt( (2*2) * (2*2) * ….) [sqrt of 6 pairs of 2]

=2*2*2*2*2*2 [6 times 2]

=64

So the solution is:

sqrt(sqrt(sqrt(4^4!))).

Rajeev Dalavi said this on Fri, 12 Mar, 2010 at 10:18 PM |

CODE is CRACKED. 🙂

This is the original solution i had in mind.

(But the other solutions here are so much more elegant)

Congrats Rajeev!! 🙂

cvs268 said this on Sat, 13 Mar, 2010 at 11:18 AM |

44 (in base 15).

rory said this on Sat, 13 Mar, 2010 at 1:20 AM |

OMG!!:-O :-OStupefyingly Mind-blowing AWESOME !!

Soooo simple, its Beautiful in itself.

AMAZING!!cvs268 said this on Sat, 13 Mar, 2010 at 11:16 AM |

64 = Re( (4^ [ pi ] ) + 4 i)where-

Re = Real part of.

[x] = Integer function (greatest integer less than x).

i.e.

Re( (4^ [ pi ] ) + 4 i)

= Re(4^3 + 4i)

= Re(64 + 4i)

= 64

(Q.E.D)

cvs268 said this on Thu, 25 Mar, 2010 at 11:51 AM |

answer 1—> 4 ^ -[tan 4!]

another—-> there u go..

4 ^ log (sqrt(sqrt(sqrt exp 4!)))

pandya said this on Thu, 01 Apr, 2010 at 2:40 AM |

4^(sqroot(4))

Gogu said this on Wed, 07 Apr, 2010 at 9:11 AM |

😦 4^2=16

NOT 64cvs268 said this on Wed, 14 Apr, 2010 at 8:53 AM |

make use of five ZERO’s and make 120. use any mathematical operations…

akshay said this on Mon, 06 Sep, 2010 at 1:39 AM |

(0!+0!+0!+0!+0!)!

sindhu said this on Thu, 26 May, 2011 at 12:10 PM |

4^2×4

manu ^^ said this on Fri, 26 Aug, 2011 at 8:25 PM |

4!!x4!!.

Duh

tyler said this on Sat, 29 Oct, 2011 at 5:33 PM |

4 factorial multiplied by 4 factorial is 24 x 24 = 5376 (not 64)

DOH! 😛 😛

CVS268 said this on Sat, 29 Oct, 2011 at 11:35 PM |